TRACE: Trajectory Recovery for Continuous Mechanism Evolution in Causal Representation Learning

2026-01-29

AI Summary

Existing causal representation learning methods typically assume that causal mechanisms switch instantaneously across discrete domains, which fails to capture the continuous evolution of mechanisms in real-world systems. This work formalizes, for the first time, a setting of continuously evolving causal mechanisms by modeling them as convex combinations of a finite set of atomic mechanisms, with time-varying mixture coefficients describing the evolution trajectory. Leveraging a Mixture-of-Experts architecture—where each expert learns one atomic mechanism—the approach jointly identifies latent causal variables and their mixing trajectories. Theoretically, both are provably identifiable under mild conditions and generalize to unseen intermediate mechanism states beyond the training distribution. Experiments on synthetic and real-world data achieve correlations up to 0.99, substantially outperforming baselines based on discrete switching assumptions.

Technology Category

• Machine Learning: Causal Learning
• Reasoning under Uncertainty: Causality
• Knowledge Representation and Reasoning: Action, Change, and Causality

Application Category

• Web Mining and Content Analysis: Models for Web evolution
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs

Abstract

Temporal causal representation learning methods assume that causal mechanisms switch instantaneously between discrete domains, yet real-world systems often exhibit continuous mechanism transitions. For example, a vehicle's dynamics evolve gradually through a turning maneuver, and human gait shifts smoothly from walking to running. We formalize this setting by modeling transitional mechanisms as convex combinations of finitely many atomic mechanisms, governed by time-varying mixing coefficients. Our theoretical contributions establish that both the latent causal variables and the continuous mixing trajectory are jointly identifiable. We further propose TRACE, a Mixture-of-Experts framework where each expert learns one atomic mechanism during training, enabling recovery of mechanism trajectories at test time. This formulation generalizes to intermediate mechanism states never observed during training. Experiments on synthetic and real-world data demonstrate that TRACE recovers mixing trajectories with up to 0.99 correlation, substantially outperforming discrete-switching baselines.

Problem

• causal representation learning
• continuous mechanism evolution
• trajectory recovery
• temporal dynamics
• mechanism transition

Innovation

• continuous causal mechanisms
• mechanism trajectory recovery
• mixture-of-experts
• causal representation learning
• identifiability